Thickness and crossing number of knots

被引:69
作者
Buck, G
Simon, J
机构
[1] St Anselms Coll, Dept Math, Manchester, NH 03102 USA
[2] Univ Iowa, Dept Math, Iowa City, IA 52242 USA
关键词
knots; thickness; rope-length; energy; crossing number;
D O I
10.1016/S0166-8641(97)00211-3
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
Given a "short" piece of rope, one can tie only "simple" knots. We make this precise by modeling "rope" as a solid tube of constant radius about a smooth care. The complexity of a knot is captured by its average crossing number which in turn bounds the minimum crossing number for the knot type. Then the ratio, L, of rope-length to radius provides an upper bound for the crossing number. Our bound is in terms of L-4/3, which we believe is the lowest exponent possible. Our route for connecting rope-length of a knot to its thickness is via self-repelling knot energies, the normal energy E-N (K) and the symmetric energy E-S(K). (C) 1999 Elsevier Science B.V. All rights reserved.
引用
收藏
页码:245 / 257
页数:13
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